A geostationary satellite maintains its orbit and attitude such that its z-axis points to a sub-satellite point or to nadir. The spacecraft control system maintains the satellite 3-axis attitude (roll, pitch, and yaw) near 0° for all three axes, typically with less than 0.1° error. The spacecraft angular rates are usually small and less than several hundred μradians/second.
The spacecraft has an Inertial Reference Unit (IRU) that provides Euler attitudes and body-fixed angular rate measurements. One representation for the Euler angle rates in terms of the body-fixed rates is:
                              [                                                                      ϕ                  .                                                                                                      θ                  .                                                                                                      ψ                  .                                                              ]                =                  [                                                                                                                ω                      x                                        ⁢                                          cos                      ⁡                                              (                        ψ                        )                                                                              -                                                            ω                      y                                        ⁢                                          sin                      ⁡                                              (                        ψ                        )                                                                                                                                                                                      ω                    e                                    +                                                            [                                                                                                    ω                            x                                                    ⁢                                                      sin                            ⁡                                                          (                              ψ                              )                                                                                                      +                                                                              ω                            y                                                    ⁢                                                      cos                            ⁡                                                          (                              ψ                              )                                                                                                                          ]                                        /                                          cos                      ⁡                                              (                        ϕ                        )                                                                                                                                                                                      ω                    z                                    +                                                            [                                                                                                    ω                            x                                                    ⁢                                                      sin                            ⁡                                                          (                              ψ                              )                                                                                                      +                                                                              ω                            y                                                    ⁢                                                      cos                            ⁡                                                          (                              ψ                              )                                                                                                                          ]                                        ⁢                                                                  sin                        ⁡                                                  (                          ϕ                          )                                                                    /                                              cos                        ⁡                                                  (                          ϕ                          )                                                                                                                                                  ]                                    (        1        )            where
φ is the spacecraft Euler roll angle
θ is the spacecraft Euler pitch angle
ψ is the spacecraft Euler yaw angle
ωe is the Earth's sidereal rate
ωx is the spacecraft x-axis angular rate
ωy is the spacecraft y-axis angular rate
ωz is the spacecraft z-axis angular rate
For small angles and for small angular rates Eq. 1 can be approximated by
                              [                                                                      ϕ                  .                                                                                                      θ                  .                                                                                                      ψ                  .                                                              ]                ≈                  [                                                                      ω                  x                                                                                                                          ω                    e                                    +                                      ω                    y                                                                                                                        ω                  z                                                              ]                                    (        2        )            
Equation 2 shows that, for small angles and small rates, the body-fixed rates measured by the IRU may be directly integrated to obtain the spacecraft attitude in terms of its Euler angles.
A scanning instrument on the spacecraft bus needs to accurately maintain its own line-of-sight in inertial space. To do so the instrument needs to compensate for any spacecraft motion. The spacecraft's inertial reference unit (IRU) provides the spacecraft's attitude and rate to the instrument. The instrument then uses the information to adjust its own line-of-sight equal and opposite to the motion of the spacecraft.
Ideally the instrument would directly use the attitude of the spacecraft as measured by the IRU to move its own line-of-sight, equal and opposite to that of the spacecraft. The attitude data provided by the IRU, unfortunately, may not be accurate enough because, for example, the spacecraft's star trackers may not be sufficiently accurate. The instrument may need more accurate spacecraft attitude data than the IRU can supply, in order to compensate for the spacecraft's motion and satisfy the instrument's line-of-sight pointing requirements.
To overcome the IRU's inadequate attitude measurements, the IRU's rate sensor data are used by the instrument, in addition to the spacecraft IRU's attitude data. Over short periods of time (for example, less than 10 minutes), the spacecraft provided IRU rate data are integrated (Eq. 2) from an initial attitude into spacecraft attitude. The instrument's attitude is, thus, more accurate because the instrument uses the more accurate body-fixed rate data instead of the less accurate IRU attitude data, over the short time period.
During integration of the IRU rate data to derive attitude data, unfortunately, errors are caused by the latency in data transfer of the rate data from the spacecraft to the instrument. Additional errors may be caused by the spacecraft's IRU dynamics. The dynamic response of the IRU rate sensor, for example one having a 10 Hz second order bandwidth, introduces an amplitude error and a phase shift to any sensed spacecraft sinusoidal motion.
As will be explained, the present invention provides a lead compensator to correct for the rate sensor dynamics and data transfer latency between (1) a sensor, such as an IRU rate sensor disposed in a vehicle (or spacecraft) and (2) an instrument, such as an imaging device disposed in the same vehicle (or spacecraft) that controls its own line-of-sight.